Sources close to the Blancos have revealed that the World Cup winner is now a top target.
They have already wrapped up deals for Eden Hazard, Luka Jovic and Ferland Mendy, freeing them to turn their attention elsewhere.
Any efforts to land Tottenham playmaker Christian Eriksen have been shelved, with Pogba now very much the man in Madrid’s sights.
He has admitted in the past to being keen on taking in a spell with the Liga giants, while the opportunity to work with fellow Frenchman Zinedine Zidane has been talked up by both sides.
“He is a great player, and Zizou knows him from Juventus. He is ready for Madrid, although he will have to prove it. That shirt weighs a lot.”
Pogba is not the only France international to be generating talk of a big-money move to Madrid.
Kylian Mbappe is a long-standing target for the Blancos and supporters at the Bernabeu are eager to see the 20-year-old lured away from Paris Saint-Germain.
Karembeu added on the chances of a deal being done there: “He is a player for Real Madrid.
“You have to sign him now! The president [Florentino Perez] knows it.
“He’s fabulous. But also very, very expensive. And you have to respect PSG.
“I hope to see Kylian playing in white one day. You must understand that there is nothing like playing in Madrid.”
Real are spending big after enduring a testing 2018-19 campaign.
Karembeu believes the right approach is being taken and is excited by the project being pieced together by Perez and Zidane.
He said: “Yes, the season was bad.
“In my time we also went from winning the Champions to suffering later. Madrid always returns.
“They have a good base, starting with the great captain, [Sergio] Ramos. The signings have been good.”